Decorrelation-Based Feature Discovery: TADPOLE-Whole

1 Effect of UPSTM-Based Decorrelation on Feature Discovery

1.0.1 Loading the libraries

library("FRESA.CAD")
library(readxl)
library(igraph)
library(umap)
library(tsne)
library(entropy)

op <- par(no.readonly = TRUE)
pander::panderOptions('digits', 3)
pander::panderOptions('table.split.table', 400)
pander::panderOptions('keep.trailing.zeros',TRUE)

1.1 Material and Methods

Data from the speech features

1.2 The data set

TADPOLE_D1_D2 <- read.csv("~/GitHub/BSWiMS/Data/TADPOLE/TADPOLE_D1_D2.csv")
TADPOLE_D1_D2_Dict <- read.csv("~/GitHub/BSWiMS/Data/TADPOLE/TADPOLE_D1_D2_Dict.csv")
TADPOLE_D1_D2_Dict_LR <- as.data.frame(read_excel("~/GitHub/BSWiMS/Data/TADPOLE/TADPOLE_D1_D2_Dict_LR.xlsx",sheet = "LeftRightFeatures"))


rownames(TADPOLE_D1_D2_Dict) <- TADPOLE_D1_D2_Dict$FLDNAME

1.3 Conditioning the data

# mm3 to mm
isVolume <- c("Ventricles","Hippocampus","WholeBrain","Entorhinal","Fusiform","MidTemp","ICV",
              TADPOLE_D1_D2_Dict$FLDNAME[str_detect(TADPOLE_D1_D2_Dict$TEXT,"Volume")]
              )


#TADPOLE_D1_D2[,isVolume] <- apply(TADPOLE_D1_D2[,isVolume],2,'^',(1/3))
TADPOLE_D1_D2[,isVolume] <- TADPOLE_D1_D2[,isVolume]^(1/3)

# mm2 to mm
isArea <- TADPOLE_D1_D2_Dict$FLDNAME[str_detect(TADPOLE_D1_D2_Dict$TEXT,"Area")]
TADPOLE_D1_D2[,isArea] <- sqrt(TADPOLE_D1_D2[,isArea])

# Get only cross sectional measurements
FreeSurfersetCross <- str_detect(colnames(TADPOLE_D1_D2),"UCSFFSX")

# The subset of baseline measurements
baselineTadpole <- subset(TADPOLE_D1_D2,VISCODE=="bl")
table(baselineTadpole$DX)

                   Dementia Dementia to MCI             MCI MCI to Dementia 
          7             336               1             864               5 
  MCI to NL              NL       NL to MCI 
          2             521               1 

table(baselineTadpole$DX_bl)

AD CN EMCI LMCI SMC 342 417 310 562 106

rownames(baselineTadpole) <- baselineTadpole$PTID


validBaselineTadpole <- cbind(DX=baselineTadpole$DX_bl,
                                 AGE=baselineTadpole$AGE,
                                 Gender=1*(baselineTadpole$PTGENDER=="Female"),
                                 ADAS11=baselineTadpole$ADAS11,
                                 ADAS13=baselineTadpole$ADAS13,
                                 MMSE=baselineTadpole$MMSE,
                                 RAVLT_immediate=baselineTadpole$RAVLT_immediate,
                                 RAVLT_learning=baselineTadpole$RAVLT_learning,
                                 RAVLT_forgetting=baselineTadpole$RAVLT_forgetting,
                                 RAVLT_perc_forgetting=baselineTadpole$RAVLT_perc_forgetting,
                                 FAQ=baselineTadpole$FAQ,
                                 Ventricles=baselineTadpole$Ventricles,
                                 Hippocampus=baselineTadpole$Hippocampus,
                                 WholeBrain=baselineTadpole$WholeBrain,
                                 Entorhinal=baselineTadpole$Entorhinal,
                                 Fusiform=baselineTadpole$Fusiform,
                                 MidTemp=baselineTadpole$MidTemp,
                                 ICV=baselineTadpole$ICV,
                                 baselineTadpole[,FreeSurfersetCross])


LeftFields <- TADPOLE_D1_D2_Dict_LR$LFN
names(LeftFields) <- LeftFields
LeftFields <- LeftFields[LeftFields %in% colnames(validBaselineTadpole)]
RightFields <- TADPOLE_D1_D2_Dict_LR$RFN
names(RightFields) <- RightFields
RightFields <- RightFields[RightFields %in% colnames(validBaselineTadpole)]

## Normalize to ICV
validBaselineTadpole$Ventricles=validBaselineTadpole$Ventricles/validBaselineTadpole$ICV
validBaselineTadpole$Hippocampus=validBaselineTadpole$Hippocampus/validBaselineTadpole$ICV
validBaselineTadpole$WholeBrain=validBaselineTadpole$WholeBrain/validBaselineTadpole$ICV
validBaselineTadpole$Entorhinal=validBaselineTadpole$Entorhinal/validBaselineTadpole$ICV
validBaselineTadpole$Fusiform=validBaselineTadpole$Fusiform/validBaselineTadpole$ICV
validBaselineTadpole$MidTemp=validBaselineTadpole$MidTemp/validBaselineTadpole$ICV

leftData <- validBaselineTadpole[,LeftFields]/validBaselineTadpole$ICV
RightData <- validBaselineTadpole[,RightFields]/validBaselineTadpole$ICV

## get mean and relative difference 
meanLeftRight <- (leftData + RightData)/2
difLeftRight <- abs(leftData - RightData)
reldifLeftRight <- difLeftRight/meanLeftRight
colnames(meanLeftRight) <- paste("M",colnames(meanLeftRight),sep="_")
colnames(difLeftRight) <- paste("D",colnames(difLeftRight),sep="_")
colnames(reldifLeftRight) <- paste("RD",colnames(reldifLeftRight),sep="_")


validBaselineTadpole <- validBaselineTadpole[,!(colnames(validBaselineTadpole) %in% 
                                               c(LeftFields,RightFields))]
#validBaselineTadpole <- cbind(validBaselineTadpole,meanLeftRight,difLeftRight,reldifLeftRight)
validBaselineTadpole <- cbind(validBaselineTadpole,meanLeftRight,difLeftRight)

## Remove columns with too many NA more than %15 of NA
nacount <- apply(is.na(validBaselineTadpole),2,sum)/nrow(validBaselineTadpole) < 0.15
diagnose <- validBaselineTadpole$DX
pander::pander(table(diagnose))

AD	CN	EMCI	LMCI	SMC
342	417	310	562	106

validBaselineTadpole <- validBaselineTadpole[,nacount]
## Remove character columns
ischar <- sapply(validBaselineTadpole,class) == "character"
validBaselineTadpole <- validBaselineTadpole[,!ischar]
## Place back diagnose
validBaselineTadpole$DX <- diagnose


validBaselineTadpole <- validBaselineTadpole[complete.cases(validBaselineTadpole),]
ischar <- sapply(validBaselineTadpole,class) == "character"
validBaselineTadpole[,!ischar] <- sapply(validBaselineTadpole[,!ischar],as.numeric)

colnames(validBaselineTadpole) <- str_remove_all(colnames(validBaselineTadpole),"_UCSFFSX_11_02_15_UCSFFSX51_08_01_16")
colnames(validBaselineTadpole) <- str_replace_all(colnames(validBaselineTadpole)," ","_")
validBaselineTadpole$LONISID <- NULL
validBaselineTadpole$IMAGEUID <- NULL
validBaselineTadpole$LONIUID <- NULL

diagnose <- as.character(validBaselineTadpole$DX)
validBaselineTadpole$DX <- diagnose
pander::pander(table(validBaselineTadpole$DX))

AD	CN	EMCI	LMCI	SMC
245	359	272	444	93

validBaselineTadpole[validBaselineTadpole$DX %in% c("EMCI","LMCI"),"DX"] <- "MCI" 
validBaselineTadpole[validBaselineTadpole$DX %in% c("CN","SMC"),"DX"] <- "NL" 

pander::pander(table(validBaselineTadpole$DX))

AD	MCI	NL
245	716	452

1.4 Get the Time To Event on MCI Subjects

subjectsID <- rownames(validBaselineTadpole)
visitsID <- unique(TADPOLE_D1_D2$VISCODE)
baseDx <- TADPOLE_D1_D2[TADPOLE_D1_D2$VISCODE=="bl",c("PTID","DX","EXAMDATE")]
rownames(baseDx) <- baseDx$PTID 
baseDx <- baseDx[subjectsID,]
lastDx <- baseDx
toDementia <- baseDx
table(lastDx$DX)

   Dementia Dementia to MCI             MCI MCI to Dementia       MCI to NL 
        244               1             711               2               2 
         NL       NL to MCI 
        452               1 

hasDementia <- lastDx$PTID[str_detect(lastDx$DX,"Dementia")]


for (vid in visitsID)
{
  DxValue <- TADPOLE_D1_D2[TADPOLE_D1_D2$VISCODE==vid,c("PTID","DX","EXAMDATE")]
  rownames(DxValue) <- DxValue$PTID 
  DxValue <- DxValue[DxValue$PTID %in% subjectsID,]
  noDX <- DxValue$PTID[nchar(DxValue$DX) < 1]
  print(length(noDX))
  DxValue[noDX,] <- lastDx[noDX,]
  inLast <- lastDx$PTID[lastDx$PTID %in% DxValue$PTID]
  print(length(inLast))
  lastDx[inLast,] <- DxValue[inLast,]
  noDementia <- !(toDementia$PTID %in% hasDementia)
  toDementia[noDementia,] <- lastDx[noDementia,]
  hasDementia <- unique(c(hasDementia,lastDx$PTID[str_detect(lastDx$DX,"Dementia")]))
}

[1] 0 [1] 1413 [1] 2 [1] 1326 [1] 6 [1] 1218 [1] 23 [1] 1095 [1] 805 [1] 1058 [1] 29 [1] 710 [1] 20 [1] 212 [1] 14 [1] 167 [1] 32 [1] 553 [1] 25 [1] 298 [1] 18 [1] 130 [1] 667 [1] 667 [1] 112 [1] 112 [1] 176 [1] 176 [1] 177 [1] 177 [1] 625 [1] 625 [1] 251 [1] 251 [1] 159 [1] 159 [1] 7 [1] 7 [1] 17 [1] 99 [1] 9 [1] 63 [1] 1 [1] 1

table(lastDx$DX)

   Dementia Dementia to MCI             MCI MCI to Dementia       MCI to NL 
        428               2             463              80               7 
         NL  NL to Dementia       NL to MCI 
        406               1              26 

baseMCI <-baseDx$PTID[baseDx$DX == "MCI"]
lastDementia <- lastDx$PTID[str_detect(lastDx$DX,"Dementia")]
lastDementia2 <- toDementia$PTID[str_detect(toDementia$DX,"Dementia")]
lastNL <- lastDx$PTID[str_detect(lastDx$DX,"NL")]

MCIatBaseline <- baseDx[baseMCI,]
MCIatEvent <- toDementia[baseMCI,]
MCIatLast <- lastDx[baseMCI,]

MCIconverters <- MCIatBaseline[baseMCI %in% lastDementia,]
MCI_No_converters <- MCIatBaseline[!(baseMCI %in% MCIconverters$PTID),]
MCIconverters$TimeToEvent <- (as.Date(toDementia[MCIconverters$PTID,"EXAMDATE"]) 
                                   - as.Date(MCIconverters$EXAMDATE))

sum(MCIconverters$TimeToEvent ==0)

[1] 0

MCIconverters$AtEventDX <- MCIatEvent[MCIconverters$PTID,"DX"]
MCIconverters$LastDX <- MCIatLast[MCIconverters$PTID,"DX"]

MCI_No_converters$TimeToEvent <- (as.Date(lastDx[MCI_No_converters$PTID,"EXAMDATE"]) 
                                   - as.Date(MCI_No_converters$EXAMDATE))

MCI_No_converters$LastDX <- MCIatLast[MCI_No_converters$PTID,"DX"]

MCI_No_converters <- subset(MCI_No_converters,TimeToEvent > 0)

2 Prognosis MCI to AD Conversion

2.1 the set

MCIPrognosisIDs <- c(MCIconverters$PTID,MCI_No_converters$PTID)

TADPOLECrossMRI <- validBaselineTadpole[MCIPrognosisIDs,]
table(TADPOLECrossMRI$DX)

MCI 680

TADPOLECrossMRI$DX <- NULL
TADPOLECrossMRI$status <- 1*(rownames(TADPOLECrossMRI) %in% MCIconverters$PTID)
table(TADPOLECrossMRI$status)

0 1 436 244

2.1.0.1 Standarize the names for the reporting

studyName <- "TADPOLE"
dataframe <- TADPOLECrossMRI
outcome <- "status"

TopVariables <- 10

thro <- 0.80
cexheat = 0.15

2.2 Generaring the report

2.2.1 Libraries

Some libraries

library(psych)
library(whitening)
library("vioplot")

2.2.2 Data specs

pander::pander(c(rows=nrow(dataframe),col=ncol(dataframe)-1))

rows	col
680	327

pander::pander(table(dataframe[,outcome]))

0	1
436	244

varlist <- colnames(dataframe)
varlist <- varlist[varlist != outcome]

largeSet <- length(varlist) > 1000

2.2.3 Scaling the data

Scaling and removing near zero variance columns and highly co-linear(r>0.99999) columns

  ### Some global cleaning
  sdiszero <- apply(dataframe,2,sd) > 1.0e-16
  dataframe <- dataframe[,sdiszero]

  varlist <- colnames(dataframe)[colnames(dataframe) != outcome]
  tokeep <- c(as.character(correlated_Remove(dataframe,varlist,thr=0.99999)),outcome)
  dataframe <- dataframe[,tokeep]

  varlist <- colnames(dataframe)
  varlist <- varlist[varlist != outcome]


dataframe <- FRESAScale(dataframe,method="OrderLogit")$scaledData

2.3 The heatmap of the data

if (!largeSet)
{
  
  hm <- heatMaps(data=dataframe,
                 Outcome=outcome,
                 Scale=TRUE,
                 hCluster = "row",
                 xlab="Feature",
                 ylab="Sample",
                 srtCol=45,
                 srtRow=45,
                 cexCol=cexheat,
                 cexRow=cexheat
                 )
  par(op)
}

2.3.0.1 Correlation Matrix of the Data

The heat map of the data

if (!largeSet)
{

  par(cex=0.6,cex.main=0.85,cex.axis=0.7)
  #cormat <- Rfast::cora(as.matrix(dataframe[,varlist]),large=TRUE)
  cormat <- cor(dataframe[,varlist],method="pearson")
  cormat[is.na(cormat)] <- 0
  gplots::heatmap.2(abs(cormat),
                    trace = "none",
  #                  scale = "row",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Original Correlation",
                    cexRow = cexheat,
                    cexCol = cexheat,
                     srtCol=45,
                     srtRow=45,
                    key.title=NA,
                    key.xlab="Pearson Correlation",
                    xlab="Feature", ylab="Feature")
  diag(cormat) <- 0
  print(max(abs(cormat)))
}

[1] 0.9997066

2.4 The decorrelation

DEdataframe <- IDeA(dataframe,verbose=TRUE,thr=thro)
#> 
#>  Included: 274 , Uni p: 0.009116418 , Uncorrelated Base: 236 , Outcome-Driven Size: 0 , Base Size: 236 
#> 
#> 
 1 <R=1.000,w=  1,N=    6>, Top: 3( 1 )[ 1 : 3 : 0.975 ]( 3 , 3 , 0 ),<|>Tot Used: 6 , Added: 3 , Zero Std: 0 , Max Cor: 0.953
#> 
 2 <R=0.953,w=  1,N=    6>, Top: 1( 1 )[ 1 : 1 : 0.951 ]( 1 , 1 , 3 ),<|>Tot Used: 8 , Added: 1 , Zero Std: 0 , Max Cor: 0.909
#> 
 3 <R=0.909,w=  2,N=    2>, Top: 1( 1 )[ 1 : 1 : 0.905 ]( 1 , 1 , 4 ),<|>Tot Used: 10 , Added: 1 , Zero Std: 0 , Max Cor: 0.900
#> 
 4 <R=0.900,w=  3,N=   18>, Top: 7( 3 )[ 1 : 7 : 0.850 ]( 7 , 9 , 5 ),<|>Tot Used: 25 , Added: 9 , Zero Std: 0 , Max Cor: 0.843
#> 
 5 <R=0.843,w=  3,N=   18>, Top: 6( 1 )[ 1 : 6 : 0.821 ]( 6 , 7 , 11 ),<|>Tot Used: 35 , Added: 7 , Zero Std: 0 , Max Cor: 0.922
#> 
 6 <R=0.922,w=  3,N=   18>, Top: 1( 1 )[ 1 : 1 : 0.861 ]( 1 , 1 , 15 ),<|>Tot Used: 36 , Added: 1 , Zero Std: 0 , Max Cor: 0.821
#> 
 7 <R=0.821,w=  4,N=   25>, Top: 12( 1 )[ 1 : 12 : 0.800 ]( 12 , 12 , 16 ),<|>Tot Used: 56 , Added: 12 , Zero Std: 0 , Max Cor: 0.962
#> 
 8 <R=0.962,w=  4,N=   25>, Top: 6( 1 )[ 1 : 6 : 0.831 ]( 6 , 6 , 24 ),<|>Tot Used: 61 , Added: 6 , Zero Std: 0 , Max Cor: 0.799
#> 
 9 <R=0.000,w=  4,N=   25>
#> 
 [ 9 ], 0.7866235 Decor Dimension: 61 . Cor to Base: 32 , ABase: 25 , Outcome Base: 0 
#> 
varlistc <- colnames(DEdataframe)[colnames(DEdataframe) != outcome]

pander::pander(sum(apply(dataframe[,varlist],2,var)))

288

pander::pander(sum(apply(DEdataframe[,varlistc],2,var)))

266

pander::pander(entropy(discretize(unlist(dataframe[,varlist]), 256)))

4.81

pander::pander(entropy(discretize(unlist(DEdataframe[,varlistc]), 256)))

4.76

2.4.1 The decorrelation matrix

if (!largeSet)
{

  par(cex=0.6,cex.main=0.85,cex.axis=0.7)
  
  UPSTM <- attr(DEdataframe,"UPSTM")
  
  gplots::heatmap.2(1.0*(abs(UPSTM)>0),
                    trace = "none",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Decorrelation matrix",
                    cexRow = cexheat,
                    cexCol = cexheat,
                   srtCol=45,
                   srtRow=45,
                    key.title=NA,
                    key.xlab="|Beta|>0",
                    xlab="Output Feature", ylab="Input Feature")
  
  par(op)
}

2.5 The heatmap of the decorrelated data

if (!largeSet)
{

  hm <- heatMaps(data=DEdataframe,
                 Outcome=outcome,
                 Scale=TRUE,
                 hCluster = "row",
                 cexRow = cexheat,
                 cexCol = cexheat,
                 srtCol=45,
                 srtRow=45,
                 xlab="Feature",
                 ylab="Sample")
  par(op)
}

2.6 The correlation matrix after decorrelation

if (!largeSet)
{

  cormat <- cor(DEdataframe[,varlistc],method="pearson")
  cormat[is.na(cormat)] <- 0
  
  gplots::heatmap.2(abs(cormat),
                    trace = "none",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Correlation after IDeA",
                    cexRow = cexheat,
                    cexCol = cexheat,
                     srtCol=45,
                     srtRow=45,
                    key.title=NA,
                    key.xlab="Pearson Correlation",
                    xlab="Feature", ylab="Feature")
  
  par(op)
  diag(cormat) <- 0
  print(max(abs(cormat)))
}

[1] 0.7992567

2.7 U-MAP Visualization of features

2.7.1 The UMAP based on LASSO on Raw Data

classes <- unique(dataframe[,outcome])
raincolors <- rainbow(length(classes))
names(raincolors) <- classes
datasetframe.umap = umap(scale(dataframe[,varlist]),n_components=2)
plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: Original",t='n')
text(datasetframe.umap$layout,labels=dataframe[,outcome],col=raincolors[dataframe[,outcome]+1])

2.7.2 The decorralted UMAP

datasetframe.umap = umap(scale(DEdataframe[,varlistc]),n_components=2)
plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: After IDeA",t='n')
text(datasetframe.umap$layout,labels=DEdataframe[,outcome],col=raincolors[DEdataframe[,outcome]+1])

2.8 Univariate Analysis

2.8.1 Univariate

univarRAW <- uniRankVar(varlist,
               paste(outcome,"~1"),
               outcome,
               dataframe,
               rankingTest="AUC")

100 : M_ST24SA 200 : D_ST49TA 300 : D_ST47CV

univarDe <- uniRankVar(varlistc,
               paste(outcome,"~1"),
               outcome,
               DEdataframe,
               rankingTest="AUC",
               )

100 : M_ST24SA 200 : D_ST49TA 300 : La_D_ST47CV

2.8.2 Final Table

univariate_columns <- c("caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC")

##topfive
topvar <- c(1:length(varlist)) <= TopVariables
pander::pander(univarRAW$orderframe[topvar,univariate_columns])

	caseMean	caseStd	controlMean	controlStd	controlKSP	ROCAUC
ADAS13	0.601	0.778	-0.2712	0.755	0.01704	0.788
ADAS11	0.614	0.924	-0.2621	0.825	0.00086	0.761
FAQ	0.832	1.082	-0.0134	0.724	0.00000	0.756
M_ST40CV	-0.579	0.905	0.2366	0.821	0.30865	0.750
M_ST29SV	-0.501	0.802	0.2761	0.859	0.31867	0.745
M_ST12SV	-0.546	0.844	0.2413	0.883	0.35129	0.744
Hippocampus	-0.489	0.805	0.2658	0.869	0.22638	0.737
RAVLT_immediate	-0.374	0.704	0.3807	0.979	0.02525	0.728
M_ST24CV	-0.568	0.959	0.2072	0.876	0.08763	0.727
M_ST31CV	-0.496	0.889	0.2225	0.864	0.74725	0.717

topLAvar <- univarDe$orderframe$Name[str_detect(univarDe$orderframe$Name,"La_")]
topLAvar <- unique(c(univarDe$orderframe$Name[topvar],topLAvar[1:as.integer(TopVariables/2)]))
finalTable <- univarDe$orderframe[topLAvar,univariate_columns]

theLaVar <- rownames(finalTable)[str_detect(rownames(finalTable),"La_")]

pander::pander(univarDe$orderframe[topLAvar,univariate_columns])

	caseMean	caseStd	controlMean	controlStd	controlKSP	ROCAUC
ADAS11	0.61418	0.924	-0.26209	0.8250	0.000860	0.761
FAQ	0.83207	1.082	-0.01340	0.7237	0.000000	0.756
M_ST40CV	-0.57880	0.905	0.23657	0.8214	0.308653	0.750
M_ST12SV	-0.54647	0.844	0.24131	0.8831	0.351289	0.744
Hippocampus	-0.48866	0.805	0.26583	0.8687	0.226377	0.737
RAVLT_immediate	-0.37368	0.704	0.38070	0.9789	0.025249	0.728
M_ST24CV	-0.56820	0.959	0.20722	0.8756	0.087630	0.727
M_ST31CV	-0.49555	0.889	0.22246	0.8643	0.747246	0.717
M_ST24TA	-0.55723	0.902	0.13997	0.8366	0.062501	0.717
WholeBrain	-0.47076	0.802	0.19530	0.8554	0.211847	0.715
La_M_ST30SV	0.18087	0.460	-0.11579	0.4949	0.948441	0.670
La_ADAS13	0.07025	0.260	-0.04456	0.2588	0.395473	0.628
La_M_ST37SV	-0.01260	0.158	-0.00361	0.0509	0.000249	0.624
La_M_ST129CV	-0.00563	0.180	-0.07611	0.2020	0.229370	0.617
La_M_ST54CV	-0.08141	0.248	-0.00370	0.2255	0.224722	0.603

dc <- getLatentCoefficients(DEdataframe)
fscores <- attr(DEdataframe,"fscore")

theSigDc <- dc[theLaVar]
names(theSigDc) <- NULL
theSigDc <- unique(names(unlist(theSigDc)))


theFormulas <- dc[rownames(finalTable)]
deFromula <- character(length(theFormulas))
names(deFromula) <- rownames(finalTable)

pander::pander(c(mean=mean(sapply(dc,length)),total=length(dc),fraction=length(dc)/(ncol(dataframe)-1)))

mean	total	fraction
2.21	33	0.101

allSigvars <- names(dc)



dx <- names(deFromula)[1]
for (dx in names(deFromula))
{
  coef <- theFormulas[[dx]]
  cname <- names(theFormulas[[dx]])
  names(cname) <- cname
  for (cf in names(coef))
  {
    if (cf != dx)
    {
      if (coef[cf]>0)
      {
        deFromula[dx] <- paste(deFromula[dx],
                               sprintf("+ %5.3f*%s",coef[cf],cname[cf]))
      }
      else
      {
        deFromula[dx] <- paste(deFromula[dx],
                               sprintf("%5.3f*%s",coef[cf],cname[cf]))
      }
    }
  }
}

finalTable <- rbind(finalTable,univarRAW$orderframe[theSigDc[!(theSigDc %in% rownames(finalTable))],univariate_columns])


orgnamez <- rownames(finalTable)
orgnamez <- str_remove_all(orgnamez,"La_")
finalTable$RAWAUC <- univarRAW$orderframe[orgnamez,"ROCAUC"]
finalTable$DecorFormula <- deFromula[rownames(finalTable)]
finalTable$fscores <- fscores[rownames(finalTable)]

Final_Columns <- c("DecorFormula","caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC","RAWAUC","fscores")

finalTable <- finalTable[order(-finalTable$ROCAUC),]
pander::pander(finalTable[,Final_Columns])

	DecorFormula	caseMean	caseStd	controlMean	controlStd	controlKSP	ROCAUC	RAWAUC	fscores
ADAS13	NA	0.60127	0.778	-0.27116	0.7548	0.017036	0.788	0.788	NA
ADAS11		0.61418	0.924	-0.26209	0.8250	0.000860	0.761	0.761	1
FAQ		0.83207	1.082	-0.01340	0.7237	0.000000	0.756	0.756	NA
M_ST40CV		-0.57880	0.905	0.23657	0.8214	0.308653	0.750	0.750	NA
M_ST12SV		-0.54647	0.844	0.24131	0.8831	0.351289	0.744	0.744	NA
Hippocampus		-0.48866	0.805	0.26583	0.8687	0.226377	0.737	0.737	1
RAVLT_immediate		-0.37368	0.704	0.38070	0.9789	0.025249	0.728	0.728	NA
M_ST24CV		-0.56820	0.959	0.20722	0.8756	0.087630	0.727	0.727	NA
M_ST31CV		-0.49555	0.889	0.22246	0.8643	0.747246	0.717	0.717	NA
M_ST24TA		-0.55723	0.902	0.13997	0.8366	0.062501	0.717	0.717	NA
WholeBrain		-0.47076	0.802	0.19530	0.8554	0.211847	0.715	0.715	NA
M_ST30SV	NA	0.36237	0.787	-0.16614	0.8160	0.069077	0.681	0.681	NA
M_ST129CV	NA	-0.37451	0.840	0.17649	0.8477	0.476195	0.680	0.680	NA
La_M_ST30SV	-0.739Ventricles + 1.000M_ST30SV	0.18087	0.460	-0.11579	0.4949	0.948441	0.670	0.681	-1
M_ST54CV	NA	-0.31614	0.763	0.14630	0.8340	0.260023	0.661	0.661	NA
M_ST129SA	NA	-0.26585	0.853	0.21936	0.8937	0.414040	0.654	0.654	1
M_ST129TA	NA	-0.31801	0.945	0.15861	0.9177	0.992539	0.643	0.643	1
M_ST54SA	NA	-0.26671	0.831	0.13560	0.9028	0.398165	0.630	0.630	1
La_ADAS13	-0.865ADAS11 + 1.000ADAS13	0.07025	0.260	-0.04456	0.2588	0.395473	0.628	0.788	-1
La_M_ST37SV	-0.998Ventricles + 1.000M_ST37SV	-0.01260	0.158	-0.00361	0.0509	0.000249	0.624	0.601	-1
La_M_ST129CV	-0.499M_ST129TA -0.791M_ST129SA + 1.000*M_ST129CV	-0.00563	0.180	-0.07611	0.2020	0.229370	0.617	0.680	-2
Ventricles	NA	0.24552	0.865	-0.06812	0.9269	0.225983	0.603	0.603	2
La_M_ST54CV	-0.461M_ST54TA -0.761M_ST54SA + 1.000*M_ST54CV	-0.08141	0.248	-0.00370	0.2255	0.224722	0.603	0.661	-2
M_ST37SV	NA	0.23236	0.863	-0.07158	0.9349	0.245853	0.601	0.601	NA
M_ST54TA	NA	-0.06906	0.935	0.10155	0.9084	0.427562	0.556	0.556	1